Is there a value of r so that x = 1, y = 2, z =...

 

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Is there a value of r so that x = 1, y = 2, z = r is a solution to the following linear system? If there is, find it. 2x+3y z = 11 x=y+2z = -7 4x + y 2z= 12 - b. (2 points, 1 point per part) Consider the following system of equations. Answer the following questions (on next page). 2x + 3y z= 0 x+ 5z = -3 y = 2z = 2 x+10y-15z = 0 i. How many equations does this system have? How many unknowns does this system have? ii. Is this system homogeneous? Briefly explain your answer (i.e., explain what you're looking for). [₁ Justify your answer. Is the matrix 4 1 0-3 ] linear combination of the matrices 10 [6] and [68] ? Is there a value of r so that x = 1, y = 2, z = r is a solution to the following linear system? If there is, find it. 2x+3y z = 11 x=y+2z = -7 4x + y 2z= 12 - b. (2 points, 1 point per part) Consider the following system of equations. Answer the following questions (on next page). 2x + 3y z= 0 x+ 5z = -3 y = 2z = 2 x+10y-15z = 0 i. How many equations does this system have? How many unknowns does this system have? ii. Is this system homogeneous? Briefly explain your answer (i.e., explain what you're looking for). [₁ Justify your answer. Is the matrix 4 1 0-3 ] linear combination of the matrices 10 [6] and [68] ?

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